{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TODO\n",
    "0. Keep working off the ball throwing example. Write code that \n",
    "  1. zooms in on a specified window\n",
    "  2. gets slope near point\n",
    "  3. plots tangent line\n",
    "1. Last time you saw continuous trajectories w/ a known equation...\n",
    "2. Which meant that we could just read off position and velocity\n",
    "3. All trajectories are continuous... but they don't have a known equation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/iroan/tools/conda3/lib/python3.6/site-packages/matplotlib/font_manager.py:278: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  'Matplotlib is building the font cache using fc-list. '\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def spring_position(t):\n",
    "    return np.exp(-t) * -np.sin(np.pi*t)\n",
    "\n",
    "def spring_velocity(t):\n",
    "    term_1 = -np.exp(-t) * np.sin(np.pi*t) \n",
    "    term_2 = np.pi * np.exp(-t) * np.cos(np.pi*t)\n",
    "    return -(term_1 + term_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0,6, 1000)\n",
    "x = np.exp(-0.5 * t) * -np.sin(np.pi * t)\n",
    "plt.plot(t,x)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_spring_motion(t_min, t_max, with_velocity=False):\n",
    "    t = np.linspace(t_min,t_max, 1000)\n",
    "    x = spring_position(t)\n",
    "    plt.plot(t,x)\n",
    "    if with_velocity:\n",
    "        v = spring_velocity(t)\n",
    "        plt.plot(t,v)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_spring_motion(0,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3Xd4VWW6/vHvkw5JgHRIIIQSegkQqqIUCzaKjWJBR8Q6Opbx6M96dGbUcSw4evQgMw5YAQsgFsSA4qCAgQRIKEmoAUIIhBRIQtr7+yN75jAYSGCXtcvzua597b2TZda9SLyz8q613iXGGJRSSvkWP6sDKKWUcj0tf6WU8kFa/kop5YO0/JVSygdp+SullA/S8ldKKR+k5a+UUj5Iy18ppXyQlr9SSvmgAKsDnE50dLRJSkqyOoZSSnmU9evXHzbGxDS1nNuWf1JSEunp6VbHUEopjyIie5qznA77KKWUD9LyV0opH6Tlr5RSPkjLXymlfJCWv1JK+SCHlL+IjBOR7SKSJyKPNvL5YBGZb/v8WhFJcsR6lVJKnRu7y19E/IE3gcuAXsBUEel1ymK3AUeNMV2BV4EX7V2vUkqpc+eIPf8hQJ4xZqcxphr4GJhwyjITgLm2158AY0VEHLDuXympqGbWd7lsOVDmjC+vlFJO9dXmAhZn7nf6ehxR/glA/knv99k+1ugyxphaoBSIOvULichMEUkXkfSioqJzCiMi/HVFrkv+8ZRSypE27yvlwQWZvPfzHurqnXt/dUeUf2N78Kembs4yGGNmG2NSjTGpMTFNXp3cqNYtAhneJYpl2QfRm9MrpTxFYVkVM+b9QlRoMG/fNAh/P6cMjvybI8p/H9DhpPftgQOnW0ZEAoDWQLED1t2ocX3asvtIBdsLy521CqWUcpjK6jpun5dOeVUtc6anEh0W7PR1OqL8fwGSRaSTiAQBU4AlpyyzBJhue30tsMI4cbf84l5xiMCyrEJnrUIppRzCGMPvP9nI5v2lzJoygJ7tWrlkvXaXv20M/15gGbAVWGCMyRaRZ0VkvG2xvwFRIpIHPAj86nRQR4oND2FQYgTfZB905mqUUspur6flsXRTAf81rgcX94pz2XodMqunMeYr4KtTPvbUSa+rgOscsa7mGtenLX/4cit7j1SQGNXSlatWSqlm+XJTAa9+l8PVAxO444LOLl23117he2nvtgAs071/pZQb2ryvlIcWZjKoYwTPX90XJ539flpeW/4dIlvSq10rHfpRSrmdovIT3D4vnajQYP73pkEEB/i7PIPXlj807P1v2HuUQ2VVVkdRSikAqmvrufuD9ZRUVjP75kEuObOnMV5d/uP6tMUY+HaLnvWjlHIPzy3dwi+7j/Lna/vTO761ZTm8uvy7xYWRFNVSx/2VUm5hwS/5vLdmDzMv6Mz4/vGWZvHq8hcRLu3Tlp93HKG0osbqOEopH5ax9yhPLMpiZHI0j1za3eo43l3+0DDuX1tvWLFdh36UUtY4VF7Fne+vJ651MH+dOoAAf+ur1/oETpbSvg1xrYL5JkuHfpRSrlddW8/d72+grLKW2Tel0qZlkNWRAB8ofz8/4dLebfkhp4jK6jqr4yilfMx/f5FN+p6jvHRdP5dN3dAcXl/+0DD0U1VTzw855zZNtFJKnYuP1+3lg7V7uePCzlzZz9oDvKfyifIf0imSNi0D9awfpZTLZOaX8NTibNsB3h5Wx/kVnyj/QH8/xvaII21rIdW19VbHUUp5uaPHq7nngw3EhDcc4HX23PznwifKHxou+CqrquXnnUesjqKU8mJ19Yb752dSVH6Ct24c6DYHeE/lM+U/MjmasOAAvtpUYHUUpZQX++uKXFblFPH0+F70a9/G6jin5TPlHxLoz9iesSzbcpCaOh36UUo53g85RcxKy+XqgQlMG5JodZwz8pnyB7i8bztKKmr4eYcO/SilHGt/SSX3f5xB97hw/jjR9VM0ny2fKv8Lu8UQGuTPV5t16Ecp5Tgnauu4+4MN1NYZ/ueGgbQIcv0UzWfLp8q/YegnjmXZOvSjlHKcPyzdysb8Ev5yXT86x4RZHadZfKr8oWHo52hFDWv0rB+llAMsytjPe2v2cPvITozr087qOM3mc+U/qrsO/SilHCOnsJzHPtvM4KQIHhnnfhdynYnPlX9IoD9jesaxLLuQWh36UUqdo2Mnarnz/fWEBgfwxrSBBLrBTJ1nw7PSOsgVfdtSfLyaNTuLrY6ilPJAxhie+Hwzuw8f5/WpKcS1CrE60lmzq/xFJFJElotIru054jTLfSMiJSKy1J71Ocqo7rG0DPLnSx36UUqdg4Xp+1iUeYD7x3ZjRJdoq+OcE3v3/B8F0owxyUCa7X1jXgJusnNdDhMS6M+YHrEsyz6oQz9KqbOSU1jOU0uyGNElinvHdLU6zjmzt/wnAHNtr+cCExtbyBiTBpTbuS6HuqJvO4qPV7N2lw79KKWap6K6lns+2EBYcACvTUlxywnbmsve8o8zxhQA2J5j7fliIjJTRNJFJL2oyLlz74/qHkuLQB36UUo139OLs8krOsZrkwcQG+554/wna7L8ReQ7Eclq5DHB0WGMMbONManGmNSYmBhHf/n/0CLInzE9Y1mWpUM/SqmmfbZhHwvX7+Pe0V05P9kzx/lPFtDUAsaYi073OREpFJF2xpgCEWkHHHJoOie7om87vtxUwLpdxYzo6vnfTKWUc+QdOsYTi7IYkhTJ/WOTrY7jEPYO+ywBptteTwcW2/n1XGq0Dv0opZpQVVPHvR9uICTQn9enDiDAw87nPx17t+IF4GIRyQUutr1HRFJFZM6/FhKRH4GFwFgR2Scil9q5Xof419DP11k6149SqnHPLt3CtoPlvHx9f9q29uxx/pM1OexzJsaYI8DYRj6eDsw46f1Ie9bjTOP7x/PlpgJ+2nGEC7s59ziDUsqzfLHxAB/absA+urtd57O4He/4+8UOo7rHEB4SwJLMA1ZHUUq5kd2Hj/PYZ5sZmNiGhy/pbnUch/P58g8O8Gdc77Z8m32Qqpo6q+MopdxAdW09v/0oA38/4a8eOG9Pc3jfFp2Dq/rHU36ilu+3e9TJSkopJ3lp2TY27y/lpWv7kdCmhdVxnELLHxjRJYrosCCWbNShH6V83aqcIt75cRc3DevIJb3bWh3HabT8gQB/Py7v2460rYc4dqLW6jhKKYscPnaCBxdspFtcGI9f0dPqOE6l5W8zvn88J2rrWb7loNVRlFIWMMbw+4UbKauq4fWpAwgJdP/78NpDy99mYGIECW1a6Fk/Svmod1fvZuX2Ip64oic92rayOo7Tafnb+PkJV/Zrx4+5hzl6vNrqOEopF8o+UMoLX2/jop5x3DSso9VxXELL/yRX9Y+ntt7wdZYO/SjlKyqqa7nvowwiQgP587X9EPHcaZrPhpb/SXrHt6JzTChLNu63OopSykWeW7qFnYeP88r1KUSGBlkdx2W0/E8iIozvH8/aXcUcLK2yOo5Sysm+2lzAR+vyueOCLpznYzP7avmf4qr+8RgDSzfpgV+lvNn+kkoe/XQT/du35qFLulkdx+W0/E/RJSaM3vGt+GKTTvOslLeqqzc88HEmdfWG16cO8MrpG5rie1vcDOP7x7Mxv4Tdh49bHUUp5QRvrMhj3e5inpvYh45RoVbHsYSWfyPGp8QjAosy9cCvUt4mfXcxs9JymJgSz9UD21sdxzJa/o1o17oFwztH8XnGfowxVsdRSjlIaWUN93+cSfuIljw3sY/VcSyl5X8akwYksOdIBRv2llgdRSnlIE8vzuJgWRWvTUkhPCTQ6jiW0vI/jcv6tiMk0I/PM/ZZHUUp5QCLM/ezKPMA941JZmBihNVxLKflfxphwQFc0qstSzcVUF2r9/dVypPtL6nkiUVZDEhswz2ju1gdxy1o+Z/BpIEJlFTUsFJv8qKUx6qvNzy0oOG0ztcmpxDgg6d1Nkb/Fc5gZNdoosOC+XyDnvWjlKea88+drNlZzDNX9fbZ0zobo+V/BgH+fozvH8+KbYcoraixOo5S6ixtOVDGS8u2c2nvOK5L9d3TOhtjV/mLSKSILBeRXNvzr46iiEiKiPwsItkisklEJtuzTle7emAC1XX1LN2s0z0o5Umqaur43fwM2rQM4vmrfWe2zuayd8//USDNGJMMpNnen6oCuNkY0xsYB7wmIm3sXK/L9I5vRXJsmA79KOVhXvxmGzmFx/jLdf19arbO5rK3/CcAc22v5wITT13AGJNjjMm1vT4AHAJi7Fyvy4gIkwYmkL7nKHuPVFgdRynVDKtyinh39W5uGZHEhd08pm5cyt7yjzPGFADYnmPPtLCIDAGCgB2n+fxMEUkXkfSioiI7oznOxJQERODzDN37V8rdHT1ezcMLN9I1NoxHL+thdRy31WT5i8h3IpLVyGPC2axIRNoB7wG3GmMaPXHeGDPbGJNqjEmNiXGf39bxbVowrFMUn2fs0+kelHJjxhge+2wzRyuqeW1yitffhN0eTZa/MeYiY0yfRh6LgUJbqf+r3Bs9IV5EWgFfAk8YY9Y4cgNcZdKABHYfqSAjX6d7UMpdfbJ+H99kH+ShS7rTJ6G11XHcmr3DPkuA6bbX04HFpy4gIkHA58A8Y8xCO9dnmcv6tiUk0I9P1ut0D0q5o71HKnhmSTZDO0Vy+8jOVsdxe/aW/wvAxSKSC1xse4+IpIrIHNsy1wMXALeISKbtkWLnel0uPCSQy/u044vMA1RW11kdRyl1ktq6eh5YkImfn/DK5BT8/fS0zqbYVf7GmCPGmLHGmGTbc7Ht4+nGmBm21+8bYwKNMSknPTIdEd7VrkvtQPmJWpZlH7Q6ilLqJG99v4P1e47yh4l9SGjTwuo4HkGv8D0LQztF0iGyBQvX51sdRSllszG/hFlpuYzvH8+ElASr43gMLf+z4OcnXDuwAz/tOEJ+sZ7zr5TVKqpreWB+JrHhwTw3wbdvznK2tPzP0jWDGvYsPt2gB36Vstofv9zKriPH+cv1/Wnd0rdvznK2tPzPUvuIlpzXJZpP1u+jvl7P+VfKKmlbC/lg7V5mjuzMiC7RVsfxOFr+5+C61PbsO1rJmp1HrI6ilE8qKj/BI59some7Vjx4STer43gkLf9zcGnvtoSHBLBQz/lXyuWMMTz66SbKT9Qya0oKwQF6Fe+50PI/ByGB/ozvH8/XWQWUVek8/0q50ofr9pK27RCPXdaDbnHhVsfxWFr+5+j61A5U1dSzdGOB1VGU8hk7io7x3NItjEyOZvrwJKvjeDQt/3PUr31rusWF6Tn/SrlITV09D8zPJCTQn79c1x8/vYrXLlr+50hEuD61Axl7S8gtLLc6jlJe7/W0XDbtK+X5SX2JaxVidRyPp+Vvh0kDEgj0Fz5ap3v/SjlT+u5i3lyZx7WD2nNZ33ZWx/EKWv52iAoL5tLebfl0wz6qanSyN6WcobyqhgcWZJIQ0YKnr+pldRyvoeVvp2lDEimtrOHrLD3wq5Qz/PcXW9h/tJJXr08hPESv4nUULX87DescRVJUSz5aq0M/Sjna15sL+GT9Pu4Z3ZXUpEir43gVLX87+fkJU4cksm53MXmH9MCvUo5SWFbFY59vpl/71tw3NtnqOF5Hy98BrhnUnkB/4UPd+1fKIerrDQ8v3EhVTR2vTk4h0F+rytH0X9QBovXAr1IONe/n3fyYe5jHr+hFl5gwq+N4JS1/B9EDv0o5Rm5hOc9/vY3R3WO4cWii1XG8lpa/g+iBX6XsV11bz/0fZxIaHMCL1/ZDRK/idRYtfwfRA79K2e/V73LYUlDGC1f3JTZcr+J1Ji1/B9IDv0qdu7U7j/D2DzuYMrgDl/Rua3Ucr6fl70B64Fepc1NWVcODCzaSGNmSJ6/Uq3hdwa7yF5FIEVkuIrm254hGlukoIutFJFNEskXkTnvW6e6mDW048PvFxgNWR1HKYzyzOJuDZVW8OjmF0OAAq+P4BHv3/B8F0owxyUCa7f2pCoARxpgUYCjwqIjE27letzW8cxTJsWHM+3kPxug9fpVqytJNB/gsYz/3ju7KwMRf7T8qJ7G3/CcAc22v5wITT13AGFNtjDlhexvsgHW6NRHh5hFJbN5fSmZ+idVxlHJrB0urePzzLPp3aMO9Y7paHcen2FvEccaYAgDbc2xjC4lIBxHZBOQDLxpjGh0TEZGZIpIuIulFRUV2RrPOpAEJhAUHMO/nPVZHUcpt/esq3urael7Tq3hdrsl/bRH5TkSyGnlMaO5KjDH5xph+QFdguojEnWa52caYVGNMakxMTPO3ws2EBQdw7aD2fLmpgKLyE03/B0r5oHd/2s0/8w7z5JW96BQdanUcn9Nk+RtjLjLG9GnksRgoFJF2ALbnQ018rQNANjDSEeHd2Y3DOlJdV8/8X/ZaHUUpt7P9YDkvfrONi3rGMnVIB6vj+CR7/85aAky3vZ4OLD51ARFpLyItbK8jgPOA7Xau1+11jQ1jZHI0H6zdS21dvdVxlHIbJ2rr+N38TFqFBPDCNXoVr1XsLf8XgItFJBe42PYeEUkVkTm2ZXoCa0VkI/AD8BdjzGY71+sRbhrWkYLSKr7bWmh1FKXcxivf5rC1oIwXr+lHdFiw1XF8ll0n1BpjjgBjG/l4OjDD9no50M+e9XiqsT3jSGjTgrk/7WFcH73vqFI/7zjC7B93Mm1oImN7NnroT7mIHl53In8/4cZhHfl55xFyCnW+H+XbSitreGhBJklRoTxxRU+r4/g8LX8nmzy4A0EBfsz9abfVUZSy1NOLsygsP8Grk1NoGaRX8VpNy9/JIkODmNA/nk837KOkotrqOEpZYnHmfhZlHuD+scmkdGhjdRyFlr9L3DayE1U19XywVk/7VL4nv7iCJz7PYmBiG+4e1cXqOMpGy98FerRtxcjkaOb+tJvqWj3tU/mO2rp6HpifCcCsKQMI0Kt43YZ+J1zktvM7caj8BF9u1tk+le94c+UO0vcc5Q+T+tAhsqXVcdRJtPxd5MJuMXSNDWPOj7t0tk/lE9bvKWZWWg6TBiQwISXB6jjqFFr+LiIi3HZ+J7IPlLF2V7HVcZRyqrKqGu7/OJOEiBY8O6G31XFUI7T8XWjSgAQiQ4OY8+Muq6Mo5VRPLcqioLSK1yYPIDwk0Oo4qhFa/i4UEujPjcM6kratkF2Hj1sdRymn+DxjH4syD3DfmGQGddSbs7grLX8Xu2lYRwL9/Hh3te79K++z90gFTy7KZnBSBPeM1tM63ZmWv4vFhAczISWehel60ZfyLrV19fxufgYi8OrkFD2t083pd8cCM0Z2prKmjvf0Tl/Ki7y+Io8Ne0v446S+tI/Q0zrdnZa/Bbq3DWdMj1je/Wk3ldV1VsdRym7rdhXzxopcrh6YwPj+8VbHUc2g5W+Ru0Z1ofh4NQvS862OopRdSitreGB+Ju0jWvLshD5Wx1HNpOVvkcFJkaR2jGD2qp3U6J2+lIcyxvDEoiwOllUxa0oKYcE6W6en0PK30F2jurC/pJKlm3TKB+WZPt2wny82HuCBi5IZkKindXoSLX8Lje4eS/e4cN76fgf19Trlg/IseYeO8eSiLIZ2iuSuUV2tjqPOkpa/hfz8hDtHdSan8Bgrth2yOo5SzVZVU8e9H26gRZA/s6YMwN9Pb8LuabT8LXZlv3gS2rTgf77P0wnflMf445db2XawnJev60/b1iFWx1HnQMvfYoH+fsy8oDMb9pawTid8Ux7g680FvLdmD7eP7MToHrFWx1HnSMvfDVyf2oGo0CDeWJlndRSlzii/uIJHPt1E//at+f2lPayOo+xgV/mLSKSILBeRXNvzaQ/3i0grEdkvIm/Ys05v1CLIn5kXdObH3MOs33PU6jhKNaqmrp77Ps4AA3+dOpCgAN139GT2fvceBdKMMclAmu396TwH/GDn+rzWTcM7EhkaxKy0XKujKNWol7/NIWNvCc9f05fEKJ2+wdPZW/4TgLm213OBiY0tJCKDgDjgWzvX57VaBgVw+8jOrMopImOv7v0r97Iqp4i3f9jB1CGJXNlPp2/wBvaWf5wxpgDA9vyroz8i4ge8DPy+qS8mIjNFJF1E0ouKiuyM5nluHt6RiJaBuvev3Mqh8ioeXJBJ97hwnr6ql9VxlIM0Wf4i8p2IZDXymNDMddwNfGWMaXISG2PMbGNMqjEmNSYmpplf3nuEBgdw+wWd+X57EZn5JVbHUYq6esMD8zM5dqKWN6YNICTQ3+pIykGanIjDGHPR6T4nIoUi0s4YUyAi7YDGrlQaDowUkbuBMCBIRI4ZY850fMBn3Tw8idmrdjLruxzevXWI1XGUj3vr+zxW5x3hxWv6khwXbnUc5UD2DvssAabbXk8HFp+6gDHmBmNMojEmCXgYmKfFf3phwQ1j/yu3F7FR9/6VhX7acZhXlucwISWe61M7WB1HOZi95f8CcLGI5AIX294jIqkiMsfecL7q5uEdadMykNe+y7E6ivJRhWVV3PdRBp1jwvjTpL6I6PQN3sau8jfGHDHGjDXGJNuei20fTzfGzGhk+X8YY+61Z52+IDwkkJkXNOz9p+/Wq36Va9XW1fPbjzI4fqKOt24YSKhO0+yV9CoNN3XriE7EhAfz52+265w/yqX+8m0O63YV8/zVOs7vzbT83VSLIH/uG9OVdbuL+T7H9057VdZYvqWQt3/YwbShiUwckGB1HOVEWv5ubPLgRDpEtuClb7brfP/K6fKLK3hoQSZ9Elrx1JV6Pr+30/J3Y0EBfjx0cXe2FJSxdHOB1XGUF6uqqeOuD9ZjgP+ZNkjP5/cBWv5ubnz/eHq0DeeVb7frvX6V0zy3dAtZ+8t45foUnbfHR2j5uzk/P+HhS7qz+0gFC9P3WR1HeaFFGfv5YO1e7rigMxf3irM6jnIRLX8PMLZnLIM6RjArLYfK6jqr4ygvsu1gGY99tpkhSZE8fGl3q+MoF9Ly9wAiwqOX9aCw7ARzftxpdRzlJUorarjjvfWEhwTwxrQBBPprHfgS/W57iMFJkVzWpy1v/bCDQ2VVVsdRHq6u3nD//AwOlFTy1o0DiW2l9+H1NVr+HuTRy3pQU1fPy9/qtA/KPq99l8P324t4+qreDOoYaXUcZQEtfw/SMSqUW0YksWB9PlsOlFkdR3moZdkH+euKPK5Pbc8NQxOtjqMsouXvYe4dk0ybFoH84cstOu2DOmt5h47x0IKN9G/fmmcn9NEJ23yYlr+Had0ikN9d1I2fdhxhxbbGbp+gVOPKq2qY+V46wQF+vHWjXsjl67T8PdC0oYl0jgnlj19tpbpWL/xSTauvNzy4YCN7jlTw5g0DiW/TwupIymJa/h4o0N+PJ67oyc6i47y7epfVcZQHmJWWy/Ithfy/y3syrHOU1XGUG9Dy91BjesRxUc84ZqXlUlBaaXUc5caWbjrArLRcrhnYnt+cl2R1HOUmtPw92NNX9aKu3vDHL7daHUW5qc37Snl44UYGdYzgT1frAV71f7T8PViHyJbcPaorSzcVsDrvsNVxlJspLKtixrxfiAoN5n9vGkRwgB7gVf9Hy9/D3XFhZxIjW/LU4iw9+Kv+raqmjpnz0imvqmXO9FSiw4KtjqTcjJa/hwsJ9OeZ8b3YoQd/lY0xht9/solN+0t5bXIKPdu1sjqSckNa/l7g5IO/+cUVVsdRFntjRR5fbDzA7y/tziW921odR7kpLX8v8cz4htvuPb4oS6/89WFfbS7g5eU5XD0ggbsu7GJ1HOXG7Cp/EYkUkeUikmt7jjjNcnUikml7LLFnnapx7SNa8sil3VmVU8SizP1Wx1EWWL+nmN/Nz7Sd2dNXz+xRZ2Tvnv+jQJoxJhlIs71vTKUxJsX2GG/nOtVp3DQ8iYGJbXj2iy0cOXbC6jjKhXYdPs6MuekktGnBOzen6tQNqkn2lv8EYK7t9Vxgop1fT9nB30944Zp+HDtRy39/scXqOMpFjhw7wS3vrkNEePeWwUSGBlkdSXkAe8s/zhhTAGB7jj3NciEiki4ia0TktL8gRGSmbbn0oqIiO6P5pm5x4dwzuitLNh5gxbZCq+MoJ6uqqWPGvHQOllYxZ3oqSdGhVkdSHqLJ8heR70Qkq5HHhLNYT6IxJhWYBrwmIo0eiTLGzDbGpBpjUmNiYs7iy6uT3T2qK93iwnj88yxKK2usjqOcpK7ecP/HGWTmlzBrSgoDExs95KZUo5osf2PMRcaYPo08FgOFItIOwPbc6BzDxpgDtuedwPfAAIdtgfqVoAA/Xrq2P4fKT/DMkmyr4ygnMKZhWo9l2YU8eUUvxvVpZ3Uk5WHsHfZZAky3vZ4OLD51ARGJEJFg2+to4DxAB6SdrH+HNtw7uiufZ+znq80FVsdRDvbWDzv4++pd3HpeEr85v5PVcZQHsrf8XwAuFpFc4GLbe0QkVUTm2JbpCaSLyEZgJfCCMUbL3wXuHdOVfu1b8/8+36w3ffciH63by5+/2c6ElHievKKX1XGUhxJ3vSAoNTXVpKenWx3D4+UdOsYVr//IiC5R/P2WwXrut4f7enMB93y4gQu6xfDOzakE+ut1muo/ich62zHWM9KfHC/XNTaMxy7rwcrtRXywdq/VcZQdVucd5v6PMxmYGMFbNwzS4ld20Z8eH3Dz8CRGJkfz3NItbC0oszqOOgcb80uYOS+dzjGh/G36YFoE6UVcyj5a/j7Az0945foUWrUI5N4PN3D8RK3VkdRZyCks55Z31xEZFsS83wyhdctAqyMpL6Dl7yNiwoOZNTmFnYeP8+TiLKvjqGbKO3SMae+sJSjAj/dvG0psqxCrIykvoeXvQ0Z0jea+Mcl8tmE/n6zfZ3Uc1YRdh48z7Z01AHx4+zA6RunVu8pxtPx9zH1jkxnWOZInF2Wx/WC51XHUaeQXVzDtnTXU1Rs+un0oXWLCrI6kvIyWv4/x9xNenzKAsJAAZr6XTmmFTv/gbvaXVDJl9hoqa+p4f8ZQkuPCrY6kvJCWvw+KbRXC2zcO5EBJJb/9OIO6eve81sMX7TtawdTZayivquH924bqLRiV02j5+6hBHSN5dkIfVuUU8dKy7VbHUcDuw8e5/u2fKamo5r3bhtInobXVkZQXC7A6gLLO1CGJZO3S8J5CAAALtklEQVQv5e0fdtA7vhVX9Y+3OpLPyi0s54Y5a6mtN3w0cxi947X4lXPpnr+Pe/qq3gxOiuDhhRvZsPeo1XF8UvaBUibPXoMB5mvxKxfR8vdxQQF+vH3jINq2DmHG3HR2Hz5udSSfkrH3KFNnryEkwI8FdwzXg7vKZbT8FVFhwfzj1iEYY7jl3XV6/18XWbntENPeWUtEaBAL7hxOJ70Ll3IhLX8FQKfoUOZMH0xBaRUz5qVTWV1ndSSvtiA9nxnz0ukSG8ond46gfURLqyMpH6Plr/5tUMcIZk1JITO/hHs+3EB1bb3VkbyOMYY3VuTyyCebGNElio9nDicmPNjqWMoHafmr/zCuTzv+MLEPK7Yd4nfzM6it018AjlJbV89Ti7P5y7c5TBqQwN+mDyYsWE+4U9bQnzz1KzcM7UhldR1/+HIrwQGbePm6/vj56U1g7FFWVcO9H2awKqeIOy7ozH+N66H/pspSWv6qUTNGdqayuo6Xl+cQHODHnyb11bI6R7sPH+e2ub+w50gFz1/dl6lDEq2OpJSWvzq9e8d0paq2jjdX7qC6tp4/X9uPAL171Fn5Ke8wd32wAT+B92cMZVjnKKsjKQVo+aszEBEevqQ7IQH+vLw8h4rqOmZNTSE4QO8i1RRjDO+u3s2fvtpKp+iGu28lRukZPcp96G6cOiMR4bdjk3nyyl58k32QmfPWU1GtdwI7k/KqGu75cAPPLt3CqO6xfHb3CC1+5Xa0/FWz3HZ+J168pi8/5hYxZfYaDpVVWR3JLW0tKGP8G6tZll3IY5f14J2bBxEeorddVO7HrvIXkUgRWS4iubbniNMslygi34rIVhHZIiJJ9qxXWWPy4ERm35RKbuExJr65mm0H9Wbw/2KM4f01e5j45mqOn6jlo9uHcceFXRDRg+TKPdm75/8okGaMSQbSbO8bMw94yRjTExgCHLJzvcoiF/WKY+Gdw6mtN1z71s+s3K7fykPlVfzmH7/wxKIshnSK5Mv7RjKkU6TVsZQ6I3vLfwIw1/Z6LjDx1AVEpBcQYIxZDmCMOWaMqbBzvcpCfRJas+ie8+gQ2ZLf/OMXXlme47M3hFmWfZBxr/3ITzuO8MxVvZh76xC9Yld5BHvLP84YUwBge45tZJluQImIfCYiGSLykog0erqIiMwUkXQRSS8qKrIzmnKm+DYt+OyuEVw9oD2vp+X63IRwReUnuO+jDO54bz3xbUL48r7zueW8TnothPIYYsyZ99hE5DugbSOfehyYa4xpc9KyR40x/zHuLyLXAn8DBgB7gfnAV8aYv51pvampqSY9Pb1ZG6GsY4xh/i/5PLUkm4iWgbx4TT9GdW9sH8A7GGNYkJ7Pn77aRmV1HfeM7spdo7oQFKDnTij3ICLrjTGpTS3X5Hn+xpiLzrCSQhFpZ4wpEJF2ND6Wvw/IMMbstP03i4BhNPxCUB5ORJgyJJE+Ca15YH4mt7z7C1OHJPL4FT29bt6arP2lPPvFFtbtLmZIp0iev7ovXWLCrI6l1Dmxd3dlCTDd9no6sLiRZX4BIkQkxvZ+DLDFzvUqN9MnoTVf/PZ87rigMx//spdxr61i5TbvOBhcWFbFwws3ctUb/ySv6BgvXtOXj28fpsWvPFqTwz5n/I9FooAFQCINQzrXGWOKRSQVuNMYM8O23MXAy4AA64GZxpjqM31tHfbxXOm7i3nk003sLDrORT3jeOrKXh55kVNJRTV/++cu5vy4i7p6w63nJXHPmK600vP2lRtr7rCPXeXvTFr+nq26tp6/r97F62m51NYbpg/vyJ0XdiEqzP3PhDl6vJo5/9zJ3J/2cOxELVf0bccj47rTMUrvtKXcn5a/cgsHS6v487JtLMrYT0igP7eel8Rvzuvklr8EdhYdY97Pe1iYnk9FTR2X92nHb8d2pUfbVlZHU6rZtPyVW8k7dIzXvsth6aYCggL8mJSSwK3nJ1lerCdq6/h+exEfrt3LDzlFBPoLV/aL565RXeimN1NXHkjLX7mlvEPlvLt6N59u2EdVTT0pHdowaUACV/Zr57K/Bmrr6lm/5yhLNh5g6aYCSitriA0P5oahHZk6tAOx4SEuyaGUM2j5K7dWUlHNgvR8Ptuwn20HywnwEwYnRXJh9xgu7BZD97hwh10wZYxh39FK1u0qZuX2Q6zKKaKsqpYWgf5c2juOiQMSOL9rtN6rQHkFLX/lMbYWlLFk4wFWbjvEtoPlALQKCaBf+zb0a9+abnHhdIhsSWJkS6JCg077S6G2rp6SyhoOlFSy6/BxdhYdZ0tBGRl7Szhsu/o4JjyYUd1iGN0jlgu7xRDqZdciKKXlrzxSYVkVq3KKyMgvYdO+ErYVlFN70rxBIhAWHECrkEAC/YU6Y6ivh+PVtZRW1nDyj7MIdIoKJSWxDQMSIxiUGEGPto77i0Ipd+SwK3yVcqW4ViFcl9qB61I7AA0HZPOLK8kvrmBvcQVHjldTVllDWVUNdfUGPxH8RGgZ5E9kaBBRYUHEtQqhc3QoHSJbEhKodx1TqjFa/sqtBQf40zU2jK6xejWtUo6kR7iUUsoHafkrpZQP0vJXSikfpOWvlFI+SMtfKaV8kJa/Ukr5IC1/pZTyQVr+Sinlg9x2egcRKQL22PElooHDDorjKXxtm31te0G32VfYs80djTExTS3ktuVvLxFJb878Ft7E17bZ17YXdJt9hSu2WYd9lFLKB2n5K6WUD/Lm8p9tdQAL+No2+9r2gm6zr3D6NnvtmL9SSqnT8+Y9f6WUUqfh0eUvIuNEZLuI5InIo418PlhE5ts+v1ZEklyf0rGasc0PisgWEdkkImki0tGKnI7U1DaftNy1ImJExOPPDGnONovI9bbvdbaIfOjqjI7WjJ/tRBFZKSIZtp/vy63I6Sgi8ncROSQiWaf5vIjI67Z/j00iMtChAYwxHvkA/IEdQGcgCNgI9DplmbuBt22vpwDzrc7tgm0eDbS0vb7LF7bZtlw4sApYA6RandsF3+dkIAOIsL2PtTq3C7Z5NnCX7XUvYLfVue3c5guAgUDWaT5/OfA1IMAwYK0j1+/Je/5DgDxjzE5jTDXwMTDhlGUmAHNtrz8BxoqIJ9/AtcltNsasNMZU2N6uAdq7OKOjNef7DPAc8GegypXhnKQ523w78KYx5iiAMeaQizM6WnO22QCtbK9bAwdcmM/hjDGrgOIzLDIBmGcarAHaiEg7R63fk8s/Acg/6f0+28caXcYYUwuUAlEuSecczdnmk91Gw56DJ2tym0VkANDBGLPUlcGcqDnf525ANxFZLSJrRGScy9I5R3O2+RngRhHZB3wF/NY10Sxztv+/nxVPvodvY3vwp5661JxlPEmzt0dEbgRSgQudmsj5zrjNIuIHvArc4qpALtCc73MADUM/o2j46+5HEeljjClxcjZnac42TwX+YYx5WUSGA+/Ztrne+fEs4dT+8uQ9/31Ah5Pet+fXfwb+exkRCaDhT8Uz/Znl7pqzzYjIRcDjwHhjzAkXZXOWprY5HOgDfC8iu2kYG13i4Qd9m/uzvdgYU2OM2QVsp+GXgadqzjbfBiwAMMb8DITQMAeOt2rW/+/nypPL/xcgWUQ6iUgQDQd0l5yyzBJguu31tcAKYzuS4qGa3GbbEMj/0lD8nj4ODE1sszGm1BgTbYxJMsYk0XCcY7wxJt2auA7RnJ/tRTQc3EdEomkYBtrp0pSO1Zxt3guMBRCRnjSUf5FLU7rWEuBm21k/w4BSY0yBo764xw77GGNqReReYBkNZwr83RiTLSLPAunGmCXA32j40zCPhj3+KdYltl8zt/klIAxYaDu2vdcYM96y0HZq5jZ7lWZu8zLgEhHZAtQBvzfGHLEutX2auc0PAe+IyAM0DH/c4sk7cyLyEQ3DdtG24xhPA4EAxpi3aTiucTmQB1QAtzp0/R78b6eUUuocefKwj1JKqXOk5a+UUj5Iy18ppXyQlr9SSvkgLX+llPJBWv5KKeWDtPyVUsoHafkrpZQP+v9NmQ88xn0gfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# how fast was it going in the very beginning?\n",
    "show_spring_motion(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_spring_motion(0, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_spring_motion(0,0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_spring_motion(0, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_spring_motion(0, 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.2\n"
     ]
    }
   ],
   "source": [
    "delta_y = (-0.0032 - 0.0000)\n",
    "delta_t = (0.0010 - 0.0000)\n",
    "speed = delta_y / delta_t\n",
    "print(speed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
